Keane has spoken about his former club's relegation plight and confidence problems since taking over from Jim Magilton at Portman Road last month,
And Sbragia - who worked for the former Manchester United captain as a coach before replacing him - appears to have taken umbrage.
"It just seems that if he wants a bit of publicity, he says something - but why not talk about Ipswich? Why is he always talking about Sunderland?" said Sbragia.
"Roy left this club. He's not here and we don't talk about him, but for some reason he keeps coming back.
"I don't know why. Maybe he still thinks he's the manager.
"Maybe he's just bored and has nothing to do, so he thinks, 'I'll have a go at Sunderland'.
"I think he should just really concentrate on Ipswich. He's back in football. He should enjoy it."
Sbragia also appeared to hint at an untold story behind Keane's departure from the Stadium of Light hot seat earlier this season, adding: "He knows the reason he left Sunderland and I know exactly why he left.
"I wouldn't want to go into print and say exactly what I know about what he said and what he did.
"But I don't know why he keeps talking about Sunderland. He has left Sunderland. I could go into more detail, but I won't."